Upthrust, also known as buoyant force, is the force exerted by a fluid on an object submerged in it. This force determines whether an object will float or sink. Understanding how to calculate upthrust is essential in physics, engineering, and daily life applications such as shipbuilding and fluid mechanics.
What is Upthrust?
Upthrust is the upward force exerted by a fluid (liquid or gas) on an object placed in it. This force opposes the weight of the object and is responsible for making objects float in water or feel lighter when submerged.
The concept of upthrust is governed by Archimedes’ Principle, which states:
“Any object wholly or partially submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by the object.“
Formula for Upthrust
The upthrust (buoyant force) on an object is given by the formula:
F_b = rho cdot V cdot g
Where:
- = Upthrust or buoyant force (Newton, N)
- = Density of the fluid (kg/m³)
- = Volume of the object submerged (m³)
- = Acceleration due to gravity (9.8 m/s²)
This formula helps calculate how much force a fluid exerts on an object, allowing us to determine if the object will float or sink.
Factors Affecting Upthrust
Several factors influence the magnitude of the upthrust force acting on an object:
1. Density of the Fluid
A fluid with higher density exerts a greater upthrust. For example, seawater (density ≈ 1025 kg/m³) provides more buoyant force than freshwater (density ≈ 1000 kg/m³).
2. Volume of the Submerged Object
The larger the volume of the object submerged, the more fluid is displaced, increasing the upthrust force.
3. Acceleration Due to Gravity
Upthrust depends on gravity, which varies slightly with location. However, on Earth, it is generally taken as 9.8 m/s².
Step-by-Step Calculation of Upthrust
To understand the calculation, let’s go through an example.
Example Problem
A wooden block with a volume of 0.02 m³ is completely submerged in freshwater (density = 1000 kg/m³). Calculate the upthrust acting on the block.
Step 1: Identify Given Values
- Volume of object, $V = 0.02$ m³
- Density of fluid, $rho = 1000$ kg/m³
- Gravity, $g = 9.8$ m/s²
Step 2: Apply the Upthrust Formula
F_b = rho cdot V cdot g
Substituting the values:
F_b = (1000) times (0.02) times (9.8)
F_b = 196 text{ N}
Step 3: Interpret the Result
The upthrust force acting on the block is 196 N. If the weight of the block is less than this force, it will float. Otherwise, it will sink.
Floating and Sinking Conditions
An object’s ability to float depends on the relationship between its weight and the upthrust acting on it.
- If Upthrust > Weight → The object floats.
- If Upthrust < Weight → The object sinks.
- If Upthrust = Weight → The object remains suspended in the fluid.
Example: Will the Block Float?
If the weight of the wooden block is calculated as:
W = m cdot g
W = (10) times (9.8) = 98 text{ N}
Since the upthrust (196 N) is greater than the block’s weight (98 N), the block will float.
Real-Life Applications of Upthrust
1. Ship Floating on Water
Ships are designed with large hollow hulls to displace more water, increasing upthrust and allowing them to float despite their heavy weight.
2. Hot Air Balloons
In gases, buoyant force also acts. Hot air inside a balloon is less dense than surrounding air, creating upthrust that lifts the balloon.
3. Submarines
Submarines control their buoyancy by adjusting the volume of water in their ballast tanks, allowing them to sink or rise.
4. Swimming and Diving
Swimmers experience upthrust, which helps them stay afloat. Wearing life jackets increases body volume, displacing more water, and increasing buoyant force.
Calculating upthrust is essential in understanding how objects interact with fluids. By using the formula F_b = ρVg, we can determine the buoyant force acting on any submerged object. The relationship between upthrust and weight determines whether an object will float, sink, or remain suspended. This principle is widely applied in engineering, marine transportation, and various industries.